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Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

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Abstract

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal, India

    K. Ramakrishnan & G. Ray

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  1. K. Ramakrishnan
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  2. G. Ray
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Correspondence to K. Ramakrishnan.

Additional information

Communicated by F.E. Udwadia.

The authors would like to thank the Associate Editor, Prof. F.E. Udwadia, and the anonymous reviewers for their constructive suggestions and helpful comments that undoubtedly contributed to the improvement of our initial submission.

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Ramakrishnan, K., Ray, G. Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay. J Optim Theory Appl 149, 366–384 (2011). https://doi.org/10.1007/s10957-010-9784-0

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